Problem: The rate of change of the perceived stimulus $p$ with respect to the measured intensity $s$ of the stimulus is inversely proportional to the intensity of the stimulus. Which equation describes this relationship? Choose 1 answer: Choose 1 answer: (Choice A) A $\dfrac{dp}{ds}=\dfrac{k}{p}$ (Choice B) B $\dfrac{ds}{dp}=\dfrac{k}{p}$ (Choice C) C $\dfrac{ds}{dp}=\dfrac{k}{s}$ (Choice D) D $\dfrac{dp}{ds}=\dfrac{k}{s}$
Solution: The perceived intensity is denoted by $p$. The rate of change of the perceived intensity, with respect to the measured intensity, is represented by $p'(s)$, or $\dfrac{dp}{ds}$. Saying that the rate of change is inversely proportional to something means it's equal to some constant $k$ divided by that thing. That thing, in our case, is the measured intensity, $s$, of the stimulus. In conclusion, the equation that describes this relationship is $\dfrac{dp}{ds}=\dfrac{k}{s}$.